Egyptian mythology is blatantly incompatible with reincarnation, as the belief in an afterlife bound to the mortal remains, and the mortuary cult resulting from this belief, was one of the most central and constant elements of Egyptian civilisation.
In fact, the Egyptians believed not in a singular soul, but in a large array of distinct souls or components of the soul, all of which were created de novo for each individual, with the main souls being ka, ba and akh.
The ka was the vital essence and what is known in religious studies as an Alter Ego. It was crafted by the potter-god Khnum during pregnancy and incarnated by a goddess of childbirth (which one varied regionally) at birth and departed into the Underworld with death, although it was still bound to the mortal remains in this world and needed sacrifices by the deceased’s family to sustain it. Its prominence diminished over the ages. Its symbol, and the emblem identifying a person’s ka, is a pair of raised arms.
The ba was the self - everything that makes a person, or even an object unique. It was a so-called “free soul”. Forming with the body during pregnancy, it was bound to the body in life, but it roamed the world freely in dreams and after death as a spirit or animal, though it, too, remained depemdamt on the physical remains. The ba could be captured, controlled and even destroyed. In the Old Kingdom, it was seen as exclusive to the king, but afterwards, it was proliferated to the general populace and increasingly became the focus. It is represented as a falcon with the head of the person in question.
The ach was a kind of ancestor spirit associated with light and the stars, animated by ba and ka after death, though it needed to be freed from the body by rituals. It had the power to affect the living world, blessing the persons descendants if they honoured them properly or punishing them if they were neglectful.
Other souls/soul components included the shadow (shut), the heart (ib) and the name (ren).
By the way, it’s rather presumptuous that to assume that you would have been a “Pharaoh or other prominent Egyptian”.